You certainly can be a world-class athlete on a vegan diet. For example, as of writing, the best weight-lifter in the USA, Kendrick Farris, is vegan. He keeps his critics quiet by breaking more records. Here are some other world-class athletes that are vegan:

Patrick Baboumian: Germany’s Strongest Man in 2011 and during 2013 he broke the world record for the most weight ever carried (video). On September 20, 2015, Baboumian beat his own world record by completing the yoke walk with 560kg in Kitzcher, Germany.

Nick Diaz and Nate Diaz, two brothers, are MMA fighters in the Ultimate Fighting Championship. Nick is the former Strikeforce champion, and Nate has plenty of accolades of his own. They're two of the highest level fighters in the world. They also do marathons and triathlons.

They're usually pescetarian, but go full vegetarian during "fight camp", which is a ~6-8 week period of ramped up intense training before a fight.